Hello again,
I agree with what you have written Gordon,
The only other thing I've come across before is a problem with the single RAM module installed.
I've known faulty memory cause freezing before. Replacement of memory would be a cheap enough to test.
I wouldn't out rule testing the hard drive via an install from the Startup disk.
Insert the startup disk 1 and hold down the C key during boot. (After the chime)
From the instal menu, sect utilities and then Disk Utility.
Select the hard drive and then options, just run disk repair.
If you was supplied with the Apple Hardware Test AHT disk then using this to help diagnose any fault would be a start.
This problem has to be hardware related, just finding which hardware device it is.
I guess if it was the Airport Card it would have a kernel panic.
If your iBook G4 has an Airport Card installed under the keyboard, try removal and booting without it.
Not saying its the problem, but worth ruling it out.
Ten years is a long time with our iBook.
I've had mine G4 for about ten years also. Been long redundant, but perfectly boxed and still works great.
Not sure I'd bother spending lots on it if it ever drastically broke down.